I'm going to avoid the gun/no gun issue for the moment and make a couple of different suggestions:
1) get some plastic squeeze bottles. Fill them with ammonia-based cleaner. With a little practice you can hit a face-sized target across the room, and you can practice with ordinary water.
2) I don't know the name of this thing, but I saw some elderly people carry them - they're an "emergency button" that hangs around your neck or clips to your belt. It's basically a cellphone. When you push the button, it calls a number and plays a message. Some call more than one number. They're used by people who have had strokes, and are likely to have them again. Stroke victims often lose the power of speech temporarily, and even if they can dial 911, the operator will give it low priority if nobody says anything.
If police response time in your area is poor - it is where I live - you might want to report a fire or heart attack instead of a burglary. Response time is usually much faster than police, and for someone unwilling to defend themself, they're probably going to need an EMT more than a cop anyway.